Item 1 MasteringPhysics 1 of 5 Item 1 A uniform steel beam has a mass of 810 kg

Question

Item 1 MasteringPhysics 1 of 5 Item 1 A uniform steel beam has a mass of 810 kg . On it is resting half of an identical beam, as shown in Tap image to zoom . Part A Determine the vertical support force at A. Express your answer to two significant figures and include the appropriate units. FA =
SubmitGive Up Part B Determine the vertical support force at B. Express your answer to two significant figures and include the appropriate units. FB =
SubmitGive Up Continue

Item 1 MasteringPhysics 1 of 5 Item 1 A uniform steel beam has a mass of 810 kg . On it is resting half of an identical beam, as shown in Tap image to zoom . Part A Determine the vertical support force at A. Express your answer to two significant figures and include the appropriate units. FA =
SubmitGive Up Part B Determine the vertical support force at B. Express your answer to two significant figures and include the appropriate units. FB =
SubmitGive Up Continue

Item 1 MasteringPhysics 1 of 5 Item 1 A uniform steel beam has a mass of 810 kg . On it is resting half of an identical beam, as shown in Tap image to zoom . Part A Determine the vertical support force at A. Express your answer to two significant figures and include the appropriate units. FA =
SubmitGive Up Part B Determine the vertical support force at B. Express your answer to two significant figures and include the appropriate units. FB =
SubmitGive Up Continue

Explanation / Answer

Find the center of mass of the two beams. Treat the load as if it were acting there.

call x=0 at left end. x=L at right end
xbar1 = L/2, m1 = 810kg
xbar2 = L/4, m2 = m1/2

xbar = (xbar1*m1+xbar2*m2)/(m1+m2)

xbar = (m1*L/2 + m1*L/8)/(m1+m1/2)

Result for COM:
xbar = 5/12*L

Call left support (RL), right support (Rr)

Add up moments about left support:
Rr*L = xbar*(m1+m1/2)*g

Solve for Rr:
Rr = 3*xbar*m1*g/(2*L)

Result for right end:
Rr = 5/8*m1*g

Add up forces to find left end reaction:
Rr + RL = (m1+m1/2)*g
Rr + RL = 3*m1*g/2
RL = 3*m1*g/2 - Rr

Substitute Rr:
RL = 3*m1*g/2 - 5/8*m1*g

Result:
RL = 7/8*m1*g

Left end reaction: RL = 7/8*m1*g
Right end reaction: Rr = 5/8*m1*g

As numbers (m1 = 810kg; g:=9.8 N/kg):
Left end reaction: RL = 6,945.75 Newtons
Right end reaction: Rr = 4,961.25 Newtons

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